Y(t)=72t-8t^2

Solution for Y(t)=72t-8t^2 equation:

(Y)=72Y-8Y^2

We move all terms to the left:

(Y)-(72Y-8Y^2)=0

We get rid of parentheses

8Y^2-72Y+Y=0

We add all the numbers together, and all the variables

8Y^2-71Y=0

a = 8; b = -71; c = 0;
Δ = b2-4ac
Δ = -712-4·8·0
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-71}{2*8}=\frac{0}{16}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+71}{2*8}=\frac{142}{16}
=8+7/8
$